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Al-Jaber, Sami M.

doi:10.1023/a:1026679921970

Cited by 44 publications

(35 citation statements)

References 10 publications

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“…In this case, the potential is the coulomb potential, The energy eigenvalues for the eigenstates of a hydrogen atom in N dimensions are given by [37] 2 2…”

Section: The Hydrogen Atom In N Dimensionsmentioning

confidence: 99%

“…This result is a natural consequence of the quantum centrifugal potential which tries to repel the particle away from the nucleus. In fact, it was pointed out by AL-Jaber [37] that the radial probability density has its maximum value when the orbital angular momentum has its maximum value ( )…”

Section: The Hydrogen Atom In N Dimensionsmentioning

confidence: 99%

“…During the past years, the generalization of three dimensional quantum problems to higher space dimensions receives a considerable development in theoretical and mathematical physics. For example, the central potentials, as hydrogen-like atoms [37]- [42] and harmonic oscillators [43]- [46] are being used as prototypes for other purposes in N-dimensional physics. Furthermore, the confined harmonic oscillator [45] and the confined hydrogen atom [47] have been discussed.…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty Relations for Some Central Potentials in N-Dimensional Space

Al-Jaber¹

2016

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We study the uncertainty relation for three quantum systems in the N-dimensional space by using the virial theorem (VT). It is shown that this relation depends on the energy spectrum of the system as well as on the space dimension N. It is pointed out that the form of lower bound of the inequality, which is governed by the ground state, depends on the system and on the space dimension N. A comparison between our result for the lower bound and recent results, based on information-theoretic approach, is pointed out. We examine and analyze these derived uncertainties for different angular momenta with a special attention made for the large N limit.

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“…In this case, the potential is the coulomb potential, The energy eigenvalues for the eigenstates of a hydrogen atom in N dimensions are given by [37] 2 2…”

Section: The Hydrogen Atom In N Dimensionsmentioning

confidence: 99%

Section: The Hydrogen Atom In N Dimensionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Uncertainty Relations for Some Central Potentials in N-Dimensional Space

Al-Jaber¹

2016

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“…which is the energy values for the Coulombic-type potential [39]. Numerical values of the energy for some diatomic molecules using the modified Kratzer-type potential (5) are given in Table I using the following potential parameters for H 2 (κ = 4.7446 eV, r e = 0.7416 Å, µ = 0.50391 amu), HCl (κ = 4.6243 eV, r e = 1.2746 Å, µ = 0.9801045 amu) and LiH (κ = 2.5181 eV, r e = 1.5956 Å, µ = 0.8801221 amu).…”

Section: Eigenvalues and Eigenfunctions Of The Mie-type Potentialmentioning

confidence: 99%

“…m N −2 . Thus by enumerating all the distinct set of m value that are possible for a given ν, the degeneracy is given by [39]: (29) and (30), results of the degeneracies of the Mie-type potentials in N -dimensions are given in Table II for N = 3-10 and n = 1-5.…”

Section: Degeneracy Of Energy Levelsmentioning

confidence: 99%

Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions

Agboola

2011

Acta Phys. Pol. A

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Electronic states and nonlinear optical properties of a two‐dimensional hexagonal quantum dot: Effects of impurity, geometrical size and confinement potential

Rezaei

Azami

Vaseghi

2012

Physica Status Solidi (b)

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Phone: þ98 741 222 3048, Fax: þ98 741 222 3048In the present work, the linear and the third-order nonlinear optical absorption coefficients as well as refractive-index changes in a two-dimensional hexagonal quantum dot with the presence of an impurity are calculated. A matrix diagonalization method is used to calculate energy levels and corresponding wave functions in the effective-mass approximation. Also, by means of the compact-density matrix approach the linear and nonlinear optical absorption coefficients and refractive-index changes are calculated. The effects of the impurity, the size of the dot and the confinement potential on energy eigenvalues, optical absorption coefficients and refractive-index changes are investigated. It is found that the energy eigenvalues, absorption coefficients and refractiveindex changes are strongly dependent on the dot size, the confinement potential and the effects produced by the impurity.

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Untitled

Cited by 44 publications

References 10 publications

Uncertainty Relations for Some Central Potentials in N-Dimensional Space

Uncertainty Relations for Some Central Potentials in N-Dimensional Space

Complete Analytical Solutions of the Mie-Type Potentials in N-Dimensions

Electronic states and nonlinear optical properties of a two‐dimensional hexagonal quantum dot: Effects of impurity, geometrical size and confinement potential

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